Finding, Hitting and Packing Cycles in Subexponential Time on Unit Disk Graphs
نویسندگان
چکیده
منابع مشابه
Finding, Hitting and Packing Cycles in Subexponential Time on Unit Disk Graphs
We give algorithms with running time 2O( √ k log k) · nO(1) for the following problems. Given an n-vertex unit disk graph G and an integer k, decide whether G contains a path on exactly/at least k vertices, a cycle on exactly k vertices, a cycle on at least k vertices, a feedback vertex set of size at most k, and a set of k pairwise vertex-disjoint cycles. For the first three problems, no subex...
متن کاملPacking Cycles in Graphs
A graph G is called cycle Mengerian (CM) if for any nonnegative integral function w de ned on V (G), the maximum number of cycles in G such that each vertex v is used at most w(v) times is equal to the minimum of Pfw(v) : v 2 Sg, where the minimum is taken over all S V (G) such that deleting S from G results a forest. The purpose of this paper is to characterize all CM graphs in terms of forbid...
متن کاملOn packing shortest cycles in graphs
We study the problems to find a maximum packing of shortest edge-disjoint cycles in a graph of given girth g (g-ESCP) and its vertex-disjoint analogue g-VSCP. In the case g = 3, Caprara and Rizzi (2001) have shown that g-ESCP can be solved in polynomial time for graphs with maximum degree 4, but is APX-hard for graphs with maximum degree 5, while g-VSCP can be solved in polynomial time for grap...
متن کاملQPTAS and Subexponential Algorithm for Maximum Clique on Disk Graphs
A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for Maximum Clique on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics ’90]. Since then, it has been an intriguing open question whether or not tractability can be extended to general disk graphs. We show the rather surprisin...
متن کاملPacking cycles in graphs, II
A graph G packs if for every induced subgraph H of G, the maximum number of vertexdisjoint cycles in H is equal to the minimum number of vertices whose deletion from H results in a forest. The purpose of this paper is to characterize all graphs that pack.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2019
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-018-00054-x